Inverse Linear Program by Modifying the Right-Hand Side Vector under l1 Norm

机译：通过修改l1范数下的右侧矢量来进行线性逆编程

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Inverse linear programming problem (ILPb) by modifying the right-hand vector is discussed in the paper. A mathematical model of (ILPb), which is an MPEC problem, is constructed based on duality theories, and then a necessary and sufficient condition of checking the feasibility of (ILPb) is provided. The inverse problem under $l_1$ norm is transformed into a problem under weighted sum-type Hamming distance with linear equality and inequality constraints. An optimal solution in the special case is also given when the dual constraint conditions are all equalities and the coefficient matrix is invertible. In this case, the system of linear equations has the only solution.

机译：本文讨论了通过修改右向量的逆线性规划问题（ILPb）。基于对偶理论，建立了一个MPEC问题（ILPb）的数学模型，然后提供了检验（ILPb）可行性的充要条件。 $ l_1 $范数下的反问题转化为加权和型汉明距离下具有线性等式和不等式约束的问题。当双重约束条件都相等且系数矩阵可逆时，还给出了在特殊情况下的最优解。在这种情况下，线性方程组是唯一的解决方案。

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《Fourth International Joint Conference on Computational Sciences and Optimization》|2011年|p.471-475|共5页
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Liu Liping; Guan Xiucui;
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中图分类计算技术、计算机技术;
关键词
$l$1 norm; Hamming distance; duality theory; inverse linear programming; right-hand side vector;

机译：$ l $ 1范数;汉明距离;对偶理论;逆线性规划;右侧向量;

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Inverse Linear Program by Modifying the Right-Hand Side Vector under l1 Norm

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